Question

The sum of two numbers is 30. The difference of the two numbers is 6. Write a system of equations to represent the situation and solve to find the numbers.

Answer 1

18, 12

Explanation:

let us say one number is x and the other one is (x+6)

x+(x+6)=30

-6

x+x=24

2x=24

divide by two

x=12

(x(12)+6)=18

Answer 2

The numbers are 18 , 12

Explanation:

Let the two numbers be x and y

The sum of the two numbers is 30.

⇒ x + y = 30 ---------------(I)

The difference of the two numbers is 6.

⇒ x - y = 6 --------------(II)

Add equations (I) and (II). Thus y will be eliminated and we can find the value of x

(I) x + y = 30

(II) x - y = 6 {Now add}

2x = 36

Divide both sides by 2

x = 36/2

x = 18

Plugin x = 18 in equation (I)

18 + y = 30

y = 30 - 18

y = 12